Express your answer as a mixed number simplified to lowest terms. $13\dfrac{2}{10}-10\dfrac{3}{4} = {?}$
Solution: Simplify each fraction. $= {13\dfrac{1}{5}} - {10\dfrac{3}{4}}$ Find a common denominator for the fractions: $= {13\dfrac{4}{20}}-{10\dfrac{15}{20}}$ Convert ${13\dfrac{4}{20}}$ to ${12 + \dfrac{20}{20} + \dfrac{4}{20}}$ So the problem becomes: ${12\dfrac{24}{20}}-{10\dfrac{15}{20}}$ Separate the whole numbers from the fractional parts: $= {12} + {\dfrac{24}{20}} - {10} - {\dfrac{15}{20}}$ Bring the whole numbers together and the fractions together: $= {12} - {10} + {\dfrac{24}{20}} - {\dfrac{15}{20}}$ Subtract the whole numbers: $=2 + {\dfrac{24}{20}} - {\dfrac{15}{20}}$ Subtract the fractions: $= 2+\dfrac{9}{20}$ Combine the whole and fractional parts into a mixed number: $= 2\dfrac{9}{20}$